Higher dimensional black holes as constrained systems

TL;DR

This paper develops a Lagrangian and Hamiltonian framework for charged black holes in higher dimensions, deriving known solutions like Reissner-Nordström without directly using Einstein's equations, potentially aiding understanding of black hole symmetries and quantum features.

Contribution

It introduces a novel formulation that simplifies deriving black hole solutions and explores their symmetries and quantum aspects in higher-dimensional contexts.

Findings

Derived charged black hole solutions without Einstein equations

Established a Hamiltonian framework for higher-dimensional black holes

Potential insights into black hole symmetries and quantum properties

Abstract

We construct a Lagrangian and Hamiltonian formulation for charged black holes in a d-dimensional maximally symmetric spherical space. By considering first new variables that give raise to an interesting dimensional reduction of the problem, we show that the introduction of a charge term is compatible with classical solutions to Einstein equations. In fact, we derive the well-known solutions for charged black holes, specially in the case of d=4, where the Reissner-Nordstr\"om solution holds, without reference to Einstein field equations. We argue that our procedure may be of help for clarifying symmetries and dynamics of black holes, as well as some quantum aspects.